Vortex complexes in two-dimensional optical lattices linearly coupled at a single site

We investigate the stability and dynamical properties of complexes consisting of two identical vortices with topological charges S = 1 and 2 in the system of two linearly on-site-coupled two-dimensional (2D) vortices. The system is mathematically modeled by two coupled nonlinear differential- difference 2D Schrödinger equations. It is found that the on-site and off-site vortices form symmetric and asymmetric complexes, respectively, with respect to the interface sites. In general, the existence regions of complexes shrink with an increase of the interlattice coupling strength. Stable symmetric complexes exist within the stability window in the parametric space whose width gradually shrinks with an increase of the interlattice coupling strength. The asymmetric vortex complexes are unstable, except in the limit of vanishing coupling between lattices.